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Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems

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Course 447: Applied Kalman Filtering with Emphasis on GPS-Aided Systems

Instructor: Mr. Michael Vaujin, Consultant
2.4 CEUs
Onsite onlyOur most requested courses are offered at different public venues two to three times per year. Most of our courses also can be taught onsite at your location. Most on-site courses can be customized to your needs. Read more about our on-site course options.

Course Description

This is a highly intensive 4-day short course on Kalman filtering theory and Kalman filtering applications. Included is a discussion of linear, extended, unscented, and square root Kalman filters and their practical applications to real-time strapdown navigation and target tracking. Exposure to Information filters, 2nd and 3rd order extended Kalman filters, particle filters, integrity monitoring, and methods of smoothing is included. Emphasis is on practical applications, but sufficient supporting theory is provided for further research. Designed for engineers who need a working knowledge of Kalman filtering or who work in the fields of navigation or target tracking.

Objectives

  • The student will receive a thorough understanding of linear, extended, unscented, and square root Kalman filters and their practical applications to real time strapdown navigation and target tracking. The student will also be exposed to Information filters, 2nd and 3rd order extended Kalman filters, particle filters, integrity monitoring, and methods of smoothing.
  • Emphasis is on practical applications, but sufficient supporting theory is provided to give attendees the necessary tools for meaningful research and development work in the field. Considerable time is devoted to modeling, the most difficult aspect of Kalman filtering, in an application setting.
  • There will be a high level of instructor/attendee interaction, designed to provide hands-on problem solving and solution discussions.

Prerequisites

  • A basic understanding of linear systems.
  • A basic understanding of probability, random variables, and stochastic processes.
  • A thorough familiarity with matrix algebra principles.

Who Should Attend?

  • Engineers who need a working knowledge of Kalman Filtering or who work in the fields of either navigation or target tracking.

Equipment You Should Bring

  • A laptop (PC or Mac) with full version of MATLAB 5.0 (or later) installed. This will allow you to work the problems in class and do the practice "homework" problems each evening. All of the problems will also be worked in class by the instructor, so this equipment is not required, but is recommended. These course notes are searchable and you can take electronic notes with the Adobe Acrobat 9 Reader we will provide you.

Materials You Will Keep

  • A color electronic copy of all course notes will be provided on a USB Drive or CD-ROM. Bringing a laptop to this class is highly recommended; power access will be provided.
  • A black and white hard copy of the course notes will also be provided.
  • Public Venue Attendees: Introduction to Random Signals and Applied Kalman Filtering, 3rd edition, by R. Grover Brown and Patrick Hwang, John Wiley & Sons, Inc., 1996. (Note: This arrangement does not apply to on-site contracts. Any books for on-site group contracts are negotiated on a case by case basis.)

Morning

Random Process Review

  • Random variables, probability densities, Gaussian and multivariate
  • Expectation, covariance matrix, random process, autocorrelation, power spectral density, stationary and nonstationary
  • Linear response, shaping filters

State Space Modeling

  • Models derived from differential equations, PSDs and block diagrams
  • Discrete time solution
  • Mean and covariance response
  • Markov and integrated Markov examples
  • Transition and process covariance

Random Process Simulation and Analysis

  • Vector random process simulation
  • Autocorrelation and PSD from data
  • Markov random process modeling and design
  • Computer demo

 

Afternoon

KF System Integration

  • Integration with complementary filtering
  • Integration examples
  • State space modeling
  • Simplified KF derivation

The Kalman Filter

  • Simplified algorithm description
  • Bias, random walk and Markov examples
  • Off-line error (covariance) analysis

Alternate Kalman Algorithms

  • State augmentation
  • Sequential processing
  • Known control inputs
  • Generalized KFs for correlated noises
  • LU decorrelation
  • Matrix partitioning for efficiency
Course: 557
Remote Course, Summer 2022

Michael is very well-versed and knowledgeable in the field of navigation, and his decades-long experience shows up in his presentation of the topic. I liked that he is able to zoom straight into the crux and motivation of the various GPS/INS techniques as well as share candidly on the practical implementation details. The Matlab examples and codes provided definitely helped in my learning.

— Name Withheld,
Course: 557
Remote Course, Summer 2022

Mike is an energetic lecturer and his many real-life examples were interesting and informative. The discussion on the different types of Kalman filters, how they differ from each other, pros and cons, and of course the sample Matlab code should prove extremely useful.

— Matthew Donn, US Navy
Course: 557
Remote Course, Summer 2022

Dr. Pue’s lectures were effective in helping me to understand the material. He did a good job of customizing the lecture for the audience based on the questions he was receiving. I can’t recommend this excellent course enough to my colleagues who work with Inertial Navigation Systems.  

— Sean Stel, L3 Harris
Course: 557
Remote Course, Summer 2022

Dr. Pue’s teaching style is excellent. His ability to explain complex concepts by relating to real-life examples was very effective.

— Mark Darnell, GE
Course: 557
Patuxent River, MD

Both instructors were very knowledgeable and had great presence. The excitement on the topics of each instructor was very evident and made it easier for me to stay engaged.

— Cameron Little, US Navy
Course: 557
Patuxent River, MD

It was very engaging and helped me learn topics that could have been tough to understand otherwise…Everything seemed relevant to our line of work.

— US Military, Name Withheld Upon Request,
Course: 335
Patuxent River, MD

I liked the teaching style – good use of time and schedule structuring, good balance of real life examples, and definitely benefitted from the knowledge and experience of the instructor.

— Mike Funya, US Navy
Course: 335
Patuxent River, MD

Dr. Betz’s teaching style kept me engaged the entire time. His knowledge, mannerisms, tone…everything kept the class interesting. It was truly a pleasure to have been a part of his class. All folks that deal with GPS signals and jamming should attend this course.

— Cameron Little, US Navy
Course: 335
Patuxent River, MD

My main objectives were to gain better knowledge on jamming in general as well as gain knowledge in the different types of bands. The course exceeded my expectations. I would recommend this to any new hires to take within two years of starting.

— Charles Kidroske, US Navy
Course: 335
Patuxent River, MD

This course did an excellent job at meeting objectives. Dr. Betz went above and beyond in providing professional guidance and specific calculations to find end result solutions.

— Eric Velez, US Navy
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